Paul Erdőos, Vance Faber, and Jean Larson Sets of natural numbers of positive density and cylindric set algebras of dimension 2. Algebra universalis, vol. 12 (1981), pp. 81–92. - Jean A. Larson The number of one-generated diagonal-free cylindric set algebras of finite dimension greater than two. Algebra universalis, vol. 16 (1983), pp. 1–16. - Jean A. Larson The number of finitely generated infinite cylindric set algebras of dimension two. Algebra universalis, vol. 19 (1984), pp. 377–396. - Jean A. Larson The number of one-generated cylindric set algebras of dimension greater than two. The journal of symbolic logic, vol. 50 (1985), pp. 59–71.

2001 ◽  
Vol 7 (2) ◽  
pp. 281-283
Author(s):  
R. D. Maddux
Keyword(s):  
Finite Dimension ◽  
Symbolic Logic ◽  
Positive Density ◽  
Natural Numbers ◽  
Finitely Generated ◽  
Dimension 2 ◽  
Cylindric Set Algebras

Sets of natural numbers of positive density and cylindric set algebras of dimension 2

1981 ◽  
Vol 12 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Paul Erdös ◽  
Vance Faber ◽  
Jean Larson
Keyword(s):  
Positive Density ◽  
Natural Numbers ◽  
Dimension 2 ◽  
Cylindric Set Algebras

scholarly journals Groups whose irreducible representations have finite degree II

1982 ◽  
Vol 25 (3) ◽  
pp. 237-243 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Characteristic Zero ◽  
Finite Dimension ◽  
Irreducible Representations ◽  
Finitely Generated ◽  
Finite Degree ◽  
Commutative Field ◽  
Soluble Groups

If F is a (commutative) field let denote the class of all groups G such that every irreducible FG-module has finite dimension over F. The introduction to [7] contains motivation for considering these classes and surveys some of the results to date concerning them. In [7] for every field F we determined the finitely generated soluble groups in . Here, for fields F of characteristic zero, we determine, at least in principle, the soluble groups in . Our main result is the following.

scholarly journals Manifolds that fail to be co-dimension 2 fibrators necessarily cover themselves

2003 ◽  
Vol 74 (1) ◽  
pp. 61-68
Author(s):  
Young Ho Im ◽  
Yongkunk Kim
Keyword(s):  
Homotopy Type ◽  
Finitely Generated ◽  
Residually Finite ◽  
Dimension 2 ◽  
Torsion Free

AbstractLetNbe a closeds-Hopfiann-manifold with residually finite, torsion free π1(N) and finiteH1(N). Suppose that either πk(N) is finitely generated for allk≥ 2, or πk(N) ≅ 0 for 1 <k<n– 1, orn≤ 4. We show that ifNfails to be a co-dimension 2 fibrator, thenNcyclically covers itself, up to homotopy type.

On the number of generators of cylindric algebras

1985 ◽  
Vol 50 (4) ◽  
pp. 865-873
Author(s):  
H. Andréka ◽  
I. Németi
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Single Element ◽  
Abstract Model ◽  
Finitely Generated ◽  
Cylindric Algebras ◽  
Abstract Model Theory ◽  
First Order ◽  
Cylindric Set Algebras

The theory of cylindric algebras (CA's) is the algebraic theory of first order logics. Several ideas about logic are easier to formulate in the frame of CA-theory. Such are e.g. some concepts of abstract model theory (cf. [1] and [10]–[12]) as well as ideas about relationships between several axiomatic theories of different similarity types (cf. [4] and [10]). In contrast with the relationship between Boolean algebras and classical propositional logic, CA's correspond not only to classical first order logic but also to several other ones. Hence CA-theoretic results contain more information than their counterparts in first order logic. For more about this see [1], [3], [5], [9], [10] and [12].Here we shall use the notation and concepts of the monographs Henkin-Monk-Tarski [7] and [8]. ω denotes the set of natural numbers. CAα denotes the class of all cylindric algebras of dimension α; by “a CAα” we shall understand an element of the class CAα. The class Dcα ⊆ CAα was defined in [7]. Note that Dcα = 0 for α ∈ ω. The classes Wsα, and Csα were defined in 1.1.1 of [8], p. 4. They are called the classes of all weak cylindric set algebras, regular cylindric set algebras and cylindric set algebras respectively. It is proved in [8] (I.7.13, I.1.9) that ⊆ CAα. (These inclusions are proper by 7.3.7, 1.4.3 and 1.5.3 of [8].)It was proved in 2.3.22 and 2.3.23 of [7] that every simple, finitely generated Dcα is generated by a single element. This is the algebraic counterpart of a property of first order logics (cf. 2.3.23 of [7]). The question arose: for which simple CAα's does “finitely generated” imply “generated by a single element” (see p. 291 and Problem 2.3 in [7]). In terms of abstract model theory this amounts to asking the question: For which logics does the property described in 2.3.23 of [7] hold? This property is roughly the following. In any maximal theory any finite set of concepts is definable in terms of a single concept. The connection with CA-theory is that maximal theories correspond to simple CA's (the elements of which are the concepts of the original logic) and definability corresponds to generation.

The number of one-generated diagonal-free cylindric set algebras of finite dimension greater than two

1983 ◽  
Vol 16 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Jean A. Larson
Keyword(s):  
Finite Dimension ◽  
Cylindric Set Algebras

Decidability of cylindric set algebras of dimension two and first-order logic with two variables

1999 ◽  
Vol 64 (4) ◽  
pp. 1563-1572 ◽  
Author(s):  
Maarten Marx ◽  
Szabolcs Mikulás
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
Universal Theory ◽  
Finite Model ◽  
Finite Model Property ◽  
First Order ◽  
Combinatorial Theorem ◽  
Finite Base ◽  
Dimension 2 ◽  
Cylindric Set Algebras

AbstractThe aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse2). The new proof also shows the known results that the universal theory of Pse2 is decidable and that every finite Pse2 can be represented on a finite base. Since the class Cs2 of cylindric set algebras of dimension 2 forms a reduct of Pse2, these results extend to Cs2 as well.

Constructing ω-stable structures: rank 2 fields

2000 ◽  
Vol 65 (1) ◽  
pp. 371-391 ◽  
Author(s):  
John T. Baldwin ◽  
Kitty Holland
Keyword(s):  
General Framework ◽  
Saturated Model ◽  
Closed Field ◽  
Morley Rank ◽  
Natural Numbers ◽  
Finitely Generated ◽  
Algebraically Closed Field ◽  
Fast Growing ◽  
Rank 2 ◽  
Stable Structures

AbstractWe provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion of separation of quantifiers which is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function μ from ‘primitive extensions’ to the natural numbers a theory Tμ of an expansion of an algebraically closed field which has Morley rank 2. Finally, we show that if μ is not finite-to-one the theory may not be ω-stable.

A group with zero homology

1968 ◽  
Vol 64 (3) ◽  
pp. 599-602 ◽  
Author(s):  
D. B. A Epstein
Keyword(s):  
Fundamental Group ◽  
Cohomological Dimension ◽  
Dimensional Manifold ◽  
Finitely Generated ◽  
3 Dimensional ◽  
Identity Group ◽  
Dimension 2

In this paper we describe a group G such that for any simple coefficients A and for any i > 0, Hi(G; A) and Hi(G; A) are zero. Other groups with this property have been found by Baumslag and Gruenberg (1). The group G in this paper has cohomological dimension 2 (that is Hi(G; A) = 0 for any i > 2 and any G-module A). G is the fundamental group of an open aspherical 3-dimensional manifold L, and is not finitely generated. The only non-trivial part of this paper is to prove that the fundamental group of the 3-manifold L, which we shall construct, is not the identity group.

The number of finitely generated infinite cylindric set algebras of dimension two

1984 ◽  
Vol 19 (3) ◽  
pp. 377-396 ◽  
Author(s):  
Jean A. Larson
Keyword(s):  
Finitely Generated ◽  
Cylindric Set Algebras
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